Based on the theory of Hilbert and Schmidt, the original spectrum is recovered with a high resolution from an integral equation representing the relation between the spectrum and its interferogram or intensity distribution given by several kinds of infrared spectrometers. The computer simulations of solving integral equations with corresponding kernels are performed. In this paper, we greatly reduce the number of calculating points ( -41) by dividing the large wave number into smaller ones and choosing appropriate parameters. The results also show that after modification of the theory of Hilbert and Schmidt, both the calculating time and the capacity of a computer are further reduced for the integral equaiton with an asymmetric kernel. Furthermore, the recovered spectrum well corresponds to the original one even when the noise of the roder of 10-4 or 10-2 is inexistence.